As you can see in the below link. Depending on where the car was leased from, Mazda Capital Services and Mazda Financial Services allow third-party buyouts. Which should save you the sales tax:
You have plenty of equity in your car with low mileage, so I would try to get quotes from all of the online vendors and local dealers (Hopefully beat the Carmax numbers). You can cash in on the 5k+ equity. Then try to find a new deal. The trade-in value would not necessarily be higher than the equity cheque you will receive from a third-party buyout. So in many cases, it might be better to just cash in on the equity and negotiate the new lease separately.